Structural Behavior of RC Column Confined by FRP Sheet under Uniaxial and Biaxial Load

Various researches have been performed to find an effective confining method using FRP sheet in order to improve the structural capacity of reinforced concrete column. However, most of these researches were undertaken for the columns subjected to concentric compressive load or fully confined RC columns. To date, it remains hard to find studies on partially FRP-confined RC columns under eccentric load. In this manner, an experimental investigation was carried out to assess the performance of rectangular RC column with different patterns of CFRP-wrap subject to eccentric loads in this paper. The experiment consists of fourteen mid-scale rectangular RC columns of 200 mm × 200 mm × 800 mm, including five controlled columns and nine CFRP-strengthened ones. All CFRP-strengthened columns were reinforced with one layer of vertical CFRP sheet with the main fiber along the axial axis at four sides, then divided into three groups according to confinement purpose, namely unconfined, partially CFRP-confined, and fully CFRP-confined group. Two loading conditions, namely uniaxially and biaxially eccentric loads, are considered as one of the test parameters. From the test of uniaxial eccentric load, partial and full CFRP-wraps provided 19% and 33% increased load-carrying capacity at an eccentricity-to-column thickness ratio (e/h) of 0.125, respectively, compared to controlled columns, and 8% and 11% at e/h = 0.25, respectively. For the partially CFRP-confined columns subjected to biaxial eccentric load with e/h = 0.125 and 0.25, the load-carrying capacities were improved by 19% and 31%, respectively. This means that the partial confinement with CFRP effectively improves the load-carrying capacity at larger biaxial eccentric load. It was found that the load-carrying capacity could be properly predicted by using code equations of ACI 440.2R-17 and Fib Bulletin 14 Guideline for the full CFRP-confined or partially CFRP-confined columns under uniaxial load. For partially CFRP-confined columns under biaxial loading, however, the safety factors using the Fib calculation process were 20% to 31% lower than that of uniaxially loaded columns.


Introduction
Reinforced concrete (RC) columns are critical structural components in building. In order to increase the load-bearing capacity and ductility of the columns, the concrete core is confined by providing lateral pressure. For improving the structural capacity of an existing column, steel jackets wrapped around the concrete cover have been used to confine RC columns. However, there are two main limitations for this method, namely the corrosion of steel and the need for prefabrication of specific column dimensions. Jacketing of RC columns with FRP (fiber reinforced polymer) sheet is an extension of the steel jacketing approach. The advantages of FRP include light weight, high stiffness, high resistance to corrosion, and easy adaptability to any shape of structural member so that it is flexibly applied through wet layup in the field. upper poor concrete part, and the height of CFRP wrapped part of column under eccentric load. It was found that partially CFRP strengthening of square column gave good results in term of loading capacity, up to 1.3 times in compare with controlled column. The study of Lewangamage et al. [13] used 17 RC specimens of 150 mm × 150 mm × 350 mm with fully and partially CFRP confinement under concentric load. Although the volumetric ratio of CFRP was kept same for all partially confined columns, it was observed that, depending on the jacket location, the strength and ductility increments would vary. The experimental results showed considerable improvements in strength (up to 83% and 100% for fully and partially confined specimens, respectively) and ductility (up to 10 and 12.7 times for fully and partially confined specimens, respectively) in comparison with controlled specimens. Turgay et al. [14] focused on the investigation of the total effect of longitudinal and transverse reinforcement of large-scale square RC columns and figured out that partial CFRP-wrapping resulted an increase in ductility of longitudinal bars. Pham et al. [15] founded that a partial wrapping arrangement changes the failure modes of specimens and the angle of failure surface.
Unfortunately, most of these researches about partial FRP-wrapping were carried out with specimens subjected to concentric compressive load. To date, it remains hard to find studies on partially FRP-confined RC columns under eccentric load. Meanwhile, the prediction of the axial load-carrying capacity of fully FRP-confined RC columns has been evaluated in contemporary design guides for RC structures strengthened with FRP sheets such as CNR-DT 200 R1/2013 [16], ACI 440.2R-17 [17], and Fib Bulletin 14 [18]. However, the axial load-carrying capacity of partially confined RC columns with FRP sheet has been present only in Fib Bulletin 14 by suggesting a reduction factor to take into account the effect of partially wrapping with FRP sheet. Therefore, there has been a lack of theorical and experimental works concerning partially FRP-wrapped RC columns under concentric load. This study carried out an experimental investigation on the performance of a rectangular RC column with different patterns of CFRP-wrap subject to uniaxial and biaxial load. The primary objectives are to (1) evaluate the CFRP strengthening efficiency of partially and fully confined RC columns under uniaxial and biaxial load; and (2) study the existing guidelines on CFRP confinement design to establish the safety factor of the predicted load-carrying capacity against the experimental results.

Specimen Design
Concentric and eccentric compressive test were planned. Fourteen mid-scale square RC columns with dimensions of 200 mm × 200 mm × 800 mm were fabricated as shown in Figure 1. These columns had identical reinforcements, including eight longitudinal 12-mm bars uniformly distributed around the perimeter (steel ratio of 2.28%). Stirrups with a diameter of 6 mm were used as a minimal requirement to minimize the additional confinement effect from the stirrups. As a result, the stirrup spacing of 100 mm was used and associated with the confining pressure (f l ) of 0.06 MPa, less than 80% of concrete compressive strength (f c '), regarding ACI 440.2R-17 [17]. Stirrups with a smaller spacing of 50 mm and 3 steel meshes (6 mm diameter with a spacing of 50 mm) were placed near two ends of the columns, and 125 mm-width CFRP sheets were also wrapped at the two ends of the columns under eccentric load to avoid local damage. The experiment includes 5 controlled columns and 9 CFRP-strengthening ones. All columns were cured at a temperature between 26 and 30 °C and humidity between 60% and 80%, within the manufacturer's recommendations. After 28 days of curing, all controlled columns were tested and used as the reference columns, and 1 layer of vertical CFRP sheet with the main fiber along the axial axis at four sides was applied to all CFRPstrengthening columns. Then, these 9 strengthened columns were divided into three groups according to confinement purpose, namely unconfined (3 columns), partially CFRP-confined (4 columns), and fully CFRP-confined (2 columns). After 7 days of adhesive curing, 3 unconfined columns were tested. Meanwhile, partially and fully CFRP-confined columns were partially and fully wrapped for concrete confinement investigation, respectively. The description of the columns' names is represented in Figure 2.

Material Properities
Concrete columns of M40 grade with the target design cubic-strength of 40 MPa were selected. The mixture design and its properties are tabulated in Table 1. The nominal diameters of longitudinal and transverse reinforcements were 12 mm and 6 mm, respectively. Carbotex UD 300 (Unidirectional Carbon Fibre Textile) by Adcos NV, Malle, Belgium as shown in Figure 3 and Carbotex Impreg (2-component solvent free epoxy system) The experiment includes 5 controlled columns and 9 CFRP-strengthening ones. All columns were cured at a temperature between 26 and 30 • C and humidity between 60% and 80%, within the manufacturer's recommendations. After 28 days of curing, all controlled columns were tested and used as the reference columns, and 1 layer of vertical CFRP sheet with the main fiber along the axial axis at four sides was applied to all CFRPstrengthening columns. Then, these 9 strengthened columns were divided into three groups according to confinement purpose, namely unconfined (3 columns), partially CFRPconfined (4 columns), and fully CFRP-confined (2 columns). After 7 days of adhesive curing, 3 unconfined columns were tested. Meanwhile, partially and fully CFRP-confined columns were partially and fully wrapped for concrete confinement investigation, respectively. The description of the columns' names is represented in Figure 2. The experiment includes 5 controlled columns and 9 CFRP-strengthening ones. All columns were cured at a temperature between 26 and 30 °C and humidity between 60% and 80%, within the manufacturer's recommendations. After 28 days of curing, all controlled columns were tested and used as the reference columns, and 1 layer of vertical CFRP sheet with the main fiber along the axial axis at four sides was applied to all CFRPstrengthening columns. Then, these 9 strengthened columns were divided into three groups according to confinement purpose, namely unconfined (3 columns), partially CFRP-confined (4 columns), and fully CFRP-confined (2 columns). After 7 days of adhesive curing, 3 unconfined columns were tested. Meanwhile, partially and fully CFRP-confined columns were partially and fully wrapped for concrete confinement investigation, respectively. The description of the columns' names is represented in Figure 2.

Material Properities
Concrete columns of M40 grade with the target design cubic-strength of 40 MPa were selected. The mixture design and its properties are tabulated in Table 1. The nominal diameters of longitudinal and transverse reinforcements were 12 mm and 6 mm, respectively. Carbotex UD 300 (Unidirectional Carbon Fibre Textile) by Adcos NV, Malle, Belgium as shown in Figure 3 and Carbotex Impreg (2-component solvent free epoxy system)

Material Properities
Concrete columns of M40 grade with the target design cubic-strength of 40 MPa were selected. The mixture design and its properties are tabulated in Table 1. The nominal diameters of longitudinal and transverse reinforcements were 12 mm and 6 mm, respectively. Carbotex UD 300 (Unidirectional Carbon Fibre Textile) by Adcos NV, Malle, Belgium as shown in Figure 3 and Carbotex Impreg (2-component solvent free epoxy system) by Adcos NV, Malle, Belgium were used in this study. The mechanical properties of reinforcements, CFRP sheets, and impregnation are tabulated in Table 2.  Fadhesive,u and Eadhesive are bond strenght and elastic module of adhesive, respectively, ffu and εfu are ultimate tensile strength and strain, respectively, tf and Ef are thickness and elastic module of CFRP, respectively, fu, fy and Es are ultimate, yield tensile strength and Elastic module of longitudinal rebars, respectively, fuw, fyw and Esw are ultimate, yield tensile strength and Elastic module of stirrup, respectively.

Strengthening with FRP Sheet
Four corners of the columns were rounded off with a radius (Rc) of 20 mm to eliminate the stress concentration and maximize the strengthening efficiency. The surface preparation was carefully performed according to the instructions of the supplier. CFRP sheets were wrapped around the perimeter of the columns with an overlapping-zone of 150 mm. Figure 4 represents the process of strengthening and curing.   F adhesive,u and E adhesive are bond strenght and elastic module of adhesive, respectively, f fu and ε fu are ultimate tensile strength and strain, respectively, t f and E f are thickness and elastic module of CFRP, respectively, f u , f y and E s are ultimate, yield tensile strength and Elastic module of longitudinal rebars, respectively, f uw , f yw and E sw are ultimate, yield tensile strength and Elastic module of stirrup, respectively.

Strengthening with FRP Sheet
Four corners of the columns were rounded off with a radius (R c ) of 20 mm to eliminate the stress concentration and maximize the strengthening efficiency. The surface preparation was carefully performed according to the instructions of the supplier. CFRP sheets were wrapped around the perimeter of the columns with an overlapping-zone of 150 mm. Figure 4 represents the process of strengthening and curing. by Adcos NV, Malle, Belgium were used in this study. The mechanical properties of reinforcements, CFRP sheets, and impregnation are tabulated in Table 2.  Fadhesive,u and Eadhesive are bond strenght and elastic module of adhesive, respectively, ffu and εfu are ultimate tensile strength and strain, respectively, tf and Ef are thickness and elastic module of CFRP, respectively, fu, fy and Es are ultimate, yield tensile strength and Elastic module of longitudinal rebars, respectively, fuw, fyw and Esw are ultimate, yield tensile strength and Elastic module of stirrup, respectively.

Strengthening with FRP Sheet
Four corners of the columns were rounded off with a radius (Rc) of 20 mm to eliminate the stress concentration and maximize the strengthening efficiency. The surface preparation was carefully performed according to the instructions of the supplier. CFRP sheets were wrapped around the perimeter of the columns with an overlapping-zone of 150 mm. Figure 4 represents the process of strengthening and curing.

Test Set Up and Installment of Equipment
All the columns were tested with an eccentric loading mechanism (except for column 00-00 under concentric loading), as shown in Figure 5. Figure 6 represents the installed specimen on the loading device. The axial and lateral displacements of the columns were monitored by seven linear variable differential transformers (LVDTs), of which three LVDTs were used for measuring the axial displacement while the remaining four LVDTs were utilized for lateral displacement at the midheight. The compressive strain of concrete was measured by two strain gauges (SGs) attached to the midheight of the columns, as shown in Figure 7. The strain of vertical CFRP sheets was measured by one SG at the extreme tension side, and those of horizontal CFRP sheets were monitored by using six SGs at three sections, including 2 SGs at each section as shown in Figure 7. The strain of longitudinal reinforcements was measured by 2 SGs at the midheight while the strain of stirrups was monitored by 2 SGs attached to midheight and one-fourth of the columns.

Test Set Up and Installment of Equipment
All the columns were tested with an eccentric loading mechanism (except for column 00-00 under concentric loading), as shown in Figure 5. Figure 6 represents the installed specimen on the loading device. The axial and lateral displacements of the columns were monitored by seven linear variable differential transformers (LVDTs), of which three LVDTs were used for measuring the axial displacement while the remaining four LVDTs were utilized for lateral displacement at the midheight. The compressive strain of concrete was measured by two strain gauges (SGs) attached to the midheight of the columns, as shown in Figure 7. The strain of vertical CFRP sheets was measured by one SG at the extreme tension side, and those of horizontal CFRP sheets were monitored by using six SGs at three sections, including 2 SGs at each section as shown in Figure 7. The strain of longitudinal reinforcements was measured by 2 SGs at the midheight while the strain of stirrups was monitored by 2 SGs attached to midheight and one-fourth of the columns.

Test Set Up and Installment of Equipment
All the columns were tested with an eccentric loading mechanism (except for column 00-00 under concentric loading), as shown in Figure 5. Figure 6 represents the installed specimen on the loading device. The axial and lateral displacements of the columns were monitored by seven linear variable differential transformers (LVDTs), of which three LVDTs were used for measuring the axial displacement while the remaining four LVDTs were utilized for lateral displacement at the midheight. The compressive strain of concrete was measured by two strain gauges (SGs) attached to the midheight of the columns, as shown in Figure 7. The strain of vertical CFRP sheets was measured by one SG at the extreme tension side, and those of horizontal CFRP sheets were monitored by using six SGs at three sections, including 2 SGs at each section as shown in Figure 7. The strain of longitudinal reinforcements was measured by 2 SGs at the midheight while the strain of stirrups was monitored by 2 SGs attached to midheight and one-fourth of the columns.

Failure Mode
The failure modes are shown in Figure 8. The unstrengthened columns exhibited three types of failure mode. For specimen 00-00 under concentrated axial load, the first crack appeared at the midheight at 45%Pu (Pu is the ultimate load) and it then developed in the axial direction towards the two ends, leading to final failure due to concrete crushing at the midheight ( Figure 8a). As shown in Figure 8b-e, for columns 00-25 and 00-50 under uniaxial loading, the first crack appeared at the flat side of the extreme compression surface around the midheight at 0.40-0.45%Pu and it then developed in the axial direction towards the two ends. Concrete crushing at the midheight caused final failure faster with larger e/h ratio. For columns 00-2525 and 00-5050 subject to biaxial loading, the first crack appeared at the extreme compression corner around the midheight at earlier load, about 0.3Pu, and it then developed in the axial direction towards the two ends. Concrete crushing at the corner around midheight caused final failure faster with larger e/h ratio. These types of failure mode are appropriate with stress concentration caused by eccentric load (around the midheight at the flat side for uniaxial loading and around the midheight at the corner for biaxial loading).

Failure Mode
The failure modes are shown in Figure 8. The unstrengthened columns exhibited three types of failure mode. For specimen 00-00 under concentrated axial load, the first crack appeared at the midheight at 45%Pu (Pu is the ultimate load) and it then developed in the axial direction towards the two ends, leading to final failure due to concrete crushing at the midheight ( Figure 8a). As shown in Figure 8b-e, for columns 00-25 and 00-50 under uniaxial loading, the first crack appeared at the flat side of the extreme compression surface around the midheight at 0.40-0.45%Pu and it then developed in the axial direction towards the two ends. Concrete crushing at the midheight caused final failure faster with larger e/h ratio. For columns 00-2525 and 00-5050 subject to biaxial loading, the first crack appeared at the extreme compression corner around the midheight at earlier load, about 0.3Pu, and it then developed in the axial direction towards the two ends. Concrete crushing at the corner around midheight caused final failure faster with larger e/h ratio. These types of failure mode are appropriate with stress concentration caused by eccentric load (around the midheight at the flat side for uniaxial loading and around the midheight at the corner for biaxial loading).

Failure Mode
The failure modes are shown in Figure 8. The unstrengthened columns exhibited three types of failure mode. For specimen 00-00 under concentrated axial load, the first crack appeared at the midheight at 45%P u (P u is the ultimate load) and it then developed in the axial direction towards the two ends, leading to final failure due to concrete crushing at the midheight ( Figure 8a). As shown in Figure 8b-e, for columns 00-25 and 00-50 under uniaxial loading, the first crack appeared at the flat side of the extreme compression surface around the midheight at 0.40-0.45%P u and it then developed in the axial direction towards the two ends. Concrete crushing at the midheight caused final failure faster with larger e/h ratio. For columns 00-2525 and 00-5050 subject to biaxial loading, the first crack appeared at the extreme compression corner around the midheight at earlier load, about 0.3P u , and it then developed in the axial direction towards the two ends. Concrete crushing at the corner around midheight caused final failure faster with larger e/h ratio. These types of failure mode are appropriate with stress concentration caused by eccentric load (around ately at CFRP sheets' rupture.
The failure modes of full confinement columns with different e/h ratio are shown in Figure 8m,n. The first crack appeared at 0.60Pu around the midheight of the extreme compression surface, and at 0.80-0.85%Pu local fracture of adhesive was found with small sound. Once fully confined columns failed, the CFRP sheets partly debonded, aand concrete between longitudinal and transverse reinforcements was partially damaged. However, it was still attached to the buckled reinforcements. This observation was also reported in a previous study on the bond of FRP sheets with various concrete strengths [19]. The debonding occurred inside a thin layer of concrete close to the interface between FRP sheet and concrete.   Cracking was heard at 0.40-0.45%P u and attributed to the local fracture of adhesive associated with the crack formation in concrete. At the ultimate load P u , CFRP sheets almost completely delaminated at midheight with damaged concrete. The failure happened at the flat side or at the corners. After failure, buckled longitudinal reinforcements were observed as shown in Figure 8f-h. In comparison with unstrengthened columns, longitudinal CFRP sheets delay the crack in the tension surface, while their effects on the compression surface are relatively small, leading to failure around the midheight at the flat side or corners, similar to unstrengthened columns' failure modes.
The failure modes of partially confined columns with different e/h ratio are shown in Figure 8i-l. The first crack appeared at 0.60-0.65P u around the midheight of the extreme compression surface, and at 0.80P u local fracture of the adhesive was found with small sound, and the rupture of CFRP sheets at the corner generated the collapse of these columns. The debonded area of the CFRP sheets was larger with higher e/h ratio. The stress on the section of partially confined columns was redistributed by transverse and longitudinal CFRP sheets, thus delaying the appearance of the first crack and increasing the ultimate load compare with unstrengthened columns. Before the failure, concrete was crushed but still in the "CFRP-sheet formwork", so that the columns collapsed immediately at CFRP sheets' rupture.
The failure modes of full confinement columns with different e/h ratio are shown in Figure 8m,n. The first crack appeared at 0.60P u around the midheight of the extreme compression surface, and at 0.80-0.85%P u local fracture of adhesive was found with small sound. Once fully confined columns failed, the CFRP sheets partly debonded, aand concrete between longitudinal and transverse reinforcements was partially damaged. However, it was still attached to the buckled reinforcements. This observation was also reported in a previous study on the bond of FRP sheets with various concrete strengths [19]. The debonding occurred inside a thin layer of concrete close to the interface between FRP sheet and concrete.

Load-Displacement Relationship
The axial load-displacement curves of the tested columns are represented in Figure 9. A summary of the test results is tabulated in Table 3. P y and P u are yielding and ultimate load, respectively. In Table 3, P u 0 is the maximum load of the controlled column 00-00. During the early loading stage 0-0.70P u , the load-displacement curves of the unstrengthened columns were linear, whereas afterward, the columns behaved in a non-linear manner, leading to a significant increase of the displacement. The yielding load, P y , is defined in Figure 10 as adopted in previous studies [20][21][22]. P y was slightly affected by the patterns of CFRP sheets, but it was considerably affected by eccentricity with the value of 64% P u for concentric load (columns 00-00) and between 84% P u and 94%P u for eccentric load as shown in Table 3. For example, the yielding loads of columns 00-25, 00-50, 00-2525, and 00-5050 were respectively 84%, 94%, 94%, and 93% of P u while the yielding loads of columns 1iC25, 1iC50, 1iC2525, and 1iC5050 were 91%, 88%, 93%, and 84% of P u , respectively.

Load-Carrying Capacity and CFRP Strengthening Efficacy
The increase of e/h ratio reduced the axial load-carrying capacity of the unstrengthened columns, e.g., the strength reductions of columns 00-25, 00-50, 00-2525, and 00-5050 were 29%, 43%, 44%, and 67% in comparison to column 00-00, as shown in Table 3. Figure 11 clearly shows the reduction of the load-carrying capacity of the columns when e/h ratio increased from 0.12 to 0.35, and the strength reduction was more pronounced for columns with e/h ratio of 0.35 as compared to columns with e/h ratio of 0.12. For instance, the load-carrying capacity of columns 00-5050 reduced by 67% and columns 00-25 exhibited a reduction of 29% regarding the controlled column 00-00, as shown in Table 3. An increase of e/h ratio significantly reduced column initial axial stiffness (EA 0 ), defined as the ratio of yielding load and corresponding axial displacement (δ y ). The reduction of the initial axial stiffness of the fully CFRP-confined columns was less than that of the unstrengthened columns (see Table 3). For instance, the decrease of the initial axial stiffness of columns 11C25 and 11C50 was respectively 33% and 40% regarding column 00-00. Meanwhile, the reduction of the initial axial stiffness of unconfined columns 00-25, 00-50, 00-2525, and 00-5050 was much larger and measured at 51%, 55%, 71%, and 75%, respectively (see Table 3). The reduction of axial stiffnesses of the partially CFRP-confined columns and unconfined columns was lower than that of the unstrengthened columns. For example, the axial stiffness reduction of columns 1iC25, 1iC50, 1iC2525, and 1iC5050 were respectively 46%, 50%, 66%, and 71% in comparison with column 00-00. For the same e/h ratio, the stiffness of fully and partially CFRP-confined columns was higher than those of unstrengthened columns. The stiffness of columns 1iC50, 1iC2525, and 11C25 was 11%, 17%, and 37% higher than that of columns 00-50, 00-2525, and 00-25, respectively. These observations mean that horizontal CFRP sheets improved column stiffness with the confinement effects.
The reduction of the axial stiffness led to a significant increase in the axial displacement (δ v ) and lateral displacement (δ hx for x direction and δ hy for y direction). The higher the e/h ratio was, the larger the ultimate displacement of the columns. At the ultimate state, the axial displacement (δ vu ) of unconfined columns 00-25, 00-50, 00-2525, and 00-5050 increased by 23%, 32%, 62%, and 73% in comparison to column 00-00. The corresponding increase of the lateral displacement of unconfined columns 00-25, 00-50, 00-2525, and 00-5050 was up to 238% regarding column 00-00. For the partially CFRP-confined columns, the maximum increment of the axial displacement of 85% was recorded for column 1iC5050 regarding column 00-00. Meanwhile, column 1iC5050 achieved the maximum lateral displacement of 236% in comparison to the reference column 00-00 (Table 3). For the fully CFRP-confined columns, increments of the axial displacement of 82% and 89% were recorded for columns 11C25 and 11C50 regarding column 00-00. As can be seen in Figure 9, at a particular applied load, the displacement increment of the partially and fully CFRP-confined columns was smaller than that of the unconfined columns and the displacement increase also reduced with a higher level of concrete confinement. In addition, the ultimate axial and lateral displacements of the partially and fully CFRP-confined columns were much higher than those of the unconfined columns. For example, the ultimate axial displacements of columns 1iC50 and 11C50 increased by 17% and 43%, and ultimate lateral displacements by 8% and 25% of columns 1iC50 and 11C50 in comparison with column 00-50, respectively. This observation indicated that CFRP sheets were very effective in improving the maximum displacement of the strengthened columns even with partial confinement.

Load-Carrying Capacity and CFRP Strengthening Efficacy
The increase of e/h ratio reduced the axial load-carrying capacity of the unstrengthened columns, e.g., the strength reductions of columns 00-25, 00-50, 00-2525, and 00-5050 were 29%, 43%, 44%, and 67% in comparison to column 00-00, as shown in Table 3. Figure 11 clearly shows the reduction of the load-carrying capacity of the columns when e/h ratio increased from 0.12 to 0.35, and the strength reduction was more pronounced for columns with e/h ratio of 0.35 as compared to columns with e/h ratio of 0.12. For instance, the load-carrying capacity of columns 00-5050 reduced by 67% and columns 00-25 exhibited a reduction of 29% regarding the controlled column 00-00, as shown in Table 3.

Load-Carrying Capacity and CFRP Strengthening Efficacy
The increase of e/h ratio reduced the axial load-carrying capacity of the unstrengthened columns, e.g., the strength reductions of columns 00-25, 00-50, 00-2525, and 00-5050 were 29%, 43%, 44%, and 67% in comparison to column 00-00, as shown in Table 3. Figure 11 clearly shows the reduction of the load-carrying capacity of the columns when e/h ratio increased from 0.12 to 0.35, and the strength reduction was more pronounced for columns with e/h ratio of 0.35 as compared to columns with e/h ratio of 0.12. For instance, the load-carrying capacity of columns 00-5050 reduced by 67% and columns 00-25 exhibited a reduction of 29% regarding the controlled column 00-00, as shown in Table 3. The increase of e/h ratio also showed a negative effect on the load-carrying capacity of the strengthened columns and the strength reduction is inversely proportional to the level of concrete confinement, e.g., unconfined, partially CFRP-confined, and fully CFRPconfined concrete. Full CFRP-wrap concrete columns increase the stiffness and ultimate displacement of the columns. Thus, the fully CFRP-confined columns experienced less strength loss than the corresponding partially CFRP-confined and unconfined concrete The increase of e/h ratio also showed a negative effect on the load-carrying capacity of the strengthened columns and the strength reduction is inversely proportional to the level of concrete confinement, e.g., unconfined, partially CFRP-confined, and fully CFRPconfined concrete. Full CFRP-wrap concrete columns increase the stiffness and ultimate displacement of the columns. Thus, the fully CFRP-confined columns experienced less strength loss than the corresponding partially CFRP-confined and unconfined concrete columns. For example, the strength reduction of fully CFRP-confined columns 11C25 and 11C50 was 6% and 36% as compared to the controlled column 00-00 (Table 3) while the strength reduction of the corresponding partially CFRP-confined columns 1iC25 and 1iC50 were 16% and 38%, respectively. At e/h = 0.25, the strength reduction of partially CFRPconfined column 1iC50 of 38% was quite closed to that of fully CFRP-confined column 11C50 of 36%. However, when real structures are exposed to a larger e/h ratio, there is a need to carry out more research on this topic towards higher e/h ratio and larger structures.
The experimental results have also shown that strengthening structures with CFRP sheets is a very effective method in providing lateral confinement to the concrete core. Figure 12 shows that the load-carrying capacity of the strengthened columns was significantly higher than that of the corresponding unstrengthened ones. The load-carrying capacity of the unconfined columns with only flexural strengthening increased by only 2-7%, while the corresponding strength improvement of the partially CFRP-confined columns ranged between 8% and 31%, and that of fully CFRP-confined columns increased 11-33% in comparison with controlled columns, as shown in Table 3. Figure 12 also shows that the difference of strengthening efficacy between partially confined columns and fully confined columns under eccentric load. For instance, the ratios P u /P u C for partially confined columns 1iC25/00-25 and 1iC50/00-50 were 1.19, and 1.08, respectively, and the ratio P u /P u C of fully CFRP-confined columns 11C25 and 11C50 were 1.33 and 1.11. Thus, it is worthy to carry out studies to further understand how the partial-CFRP-wrap contributes to the load-carrying capacity of these columns. columns. For example, the strength reduction of fully CFRP-confined columns 11C25 and 11C50 was 6% and 36% as compared to the controlled column 00-00 (Table 3) while the strength reduction of the corresponding partially CFRP-confined columns 1iC25 and 1iC50 were 16% and 38%, respectively. At e/h = 0.25, the strength reduction of partially CFRP-confined column 1iC50 of 38% was quite closed to that of fully CFRPconfined column 11C50 of 36%. However, when real structures are exposed to a larger e/h ratio, there is a need to carry out more research on this topic towards higher e/h ratio and larger structures. The experimental results have also shown that strengthening structures with CFRP sheets is a very effective method in providing lateral confinement to the concrete core. Figure 12 shows that the load-carrying capacity of the strengthened columns was significantly higher than that of the corresponding unstrengthened ones. The load-carrying capacity of the unconfined columns with only flexural strengthening increased by only 2-7%, while the corresponding strength improvement of the partially CFRP-confined columns ranged between 8% and 31%, and that of fully CFRP-confined columns increased 11-33% in comparison with controlled columns, as shown in Table 3. Figure 12 also shows that the difference of strengthening efficacy between partially confined columns and fully confined columns under eccentric load. For instance, the ratios Pu/Pu C for partially confined columns 1iC25/00-25 and 1iC50/00-50 were 1.19, and 1.08, respectively, and the ratio Pu/Pu C of fully CFRP-confined columns 11C25 and 11C50 were 1.33 and 1.11. Thus, it is worthy to carry out studies to further understand how the partial-CFRP-wrap contributes to the load-carrying capacity of these columns.  Figures 13-16 show the relationship between the applied load and strain of CFRP sheets and reinforcements. The strains of rebars in all specimens are tabulated in Table 4. As shown in Figure 13 and Table 4, the ultimate strain of vertical CFRP sheets (εfvu) increased with the level of confinement. For example, the ultimate strain of partially CFRPconfined columns 1iC50, 1iC2525, and 1iC5050 increased 81%, 30%, and 81% regarding the corresponding unconfined columns 10C50, 10C2525, and 10C5050, respectively. The increase of vertical-CFRP-sheet ultimate strain of fully CFRP-confined columns were higher, up to 138% for column 11C50 regarding column 10C50. The ultimate strains of transverse CFRP sheets of fully CFRP-confined columns were higher than that of partially CFRP-confined columns. At the extremely compressive side (side B), the increases of εfhu,B were about 5% to 18%, and at the extreme tension side (side A), these increases of εfhu,A   Table 4. As shown in Figure 13 and Table 4, the ultimate strain of vertical CFRP sheets (ε fvu ) increased with the level of confinement. For example, the ultimate strain of partially CFRP-confined columns 1iC50, 1iC2525, and 1iC5050 increased 81%, 30%, and 81% regarding the corresponding unconfined columns 10C50, 10C2525, and 10C5050, respectively. The increase of vertical-CFRP-sheet ultimate strain of fully CFRP-confined columns were higher, up to 138% for column 11C50 regarding column 10C50. The ultimate strains of transverse CFRP sheets of fully CFRP-confined columns were higher than that of partially CFRP-confined columns. At the extremely compressive side (side B), the increases of ε fhu,B were about 5% to 18%, and at the extreme tension side (side A), these increases of ε fhu,A were much higher, up to 21-89%. This phenomenon is due to the better strain distribution of fully CFRP-wrapped columns than partially CFRP-wrapped ones. When e/h ratio increases, ε fhu,A at extremely tension side becomes smaller and approaches zero for both the full and partial wrap. The CFRP strains at ultimate stage were about 0.92% and 0.99% for partially CFRP-wrapped columns and about 1.09-1.13% for fully CFRP-wrapped ones. These ultimate CFRP strains of partially and fully CFRP-wrapped columns correspond to 44-48% and 52-54% of CFRP nominal rupture strain determined from the flat coupon tests, respectively. The range of full wrap columns was inside the range between 51% and 78% of the nominal rupture strain reported by Lam and Teng [23] for fully CFRP-confined square columns, and that of partial wrap columns was slightly lower than the range between 51% and 78%. This observation indicated that partial CFRP-wrap was acceptable in term of developing CFRP tension capacity. partial CFRP-wrap was acceptable in term of developing CFRP tension capacity.

Strain of CFRP Sheets and Steel Reinforcements
In addition, Figure 14 also shows that stirrups of the unstrengthened columns and unconfined columns did not yield at the ultimate stage. Particularly, stirrups of columns 00-00 under concentric loads yielded at 0.98Pu. This was because the deformation of the unstrengthened and unconfined columns was significantly lower than that of the strengthened columns. Therefore, these columns might fail before yielding stirrups. Meanwhile, stirrups of the partially and fully CFRP-confined columns yielded at the loading level of 0.96-0.99Pu thanks to the confinement effect. These observations have proven the interaction between CFRP and stirrups. The ultimate strain of stirrups of the partially and fully CFRP-confined columns was 1.6-2.0 and 1.8-2.4 times of that of the unstrengthened ones, respectively. These observations demonstrated that the use of partial-CFRPwrap significantly affected the lateral displacement of the columns.    The longitudinal compressive rebars of the unstrengthened columns yielded at the load level of 0.93-1.00Pu ( Figure 15). There, ultimate strain varied between 0.18% and 0.22% and it reduced with high e/h ratio. Meanwhile, the partially and fully CFRP-confined columns had longitudinal reinforcements yielding at the load level of 0.81-0.96Pu, and 0.80-0.85Pu, respectively. The ultimate strain of the longitudinal compressive reinforcements of unconfined, partially CFRP-confined, and fully CFRP-confined columns  In addition, Figure 16 also shows that the longitudinal tension rebars of the unstrengthened and unconfined columns did not yield at the ultimate stage. Particularly, longitudinal tension rebars of column 00-5050 yielded at 0.89Pu due high value of e/h ratio. This was because the deformation of these columns was significantly lower than that of the strengthened columns. Therefore, these columns might fail before yielding of longitudinal tension reinforcement and it was dependent on e/h ratio. As shown in Table 3, the longitudinal tension rebar strain of unconfined columns was even lower, achieving about 48-93% that of the corresponding controlled columns. The reason for this is that vertical CFRP sheets at the tension side work together with tension rebars. Meanwhile, longitudinaltension-rebars of the partially and fully CFRP-confined columns yielded at the loading level of 0.72-0.96Pu and 0.80-0.85Pu, respectively. The use of CFRP wrap for confinement significantly reduced the axial deformation of the columns and thus delayed the yielding of longitudinal rebars as compared to the unstrengthened and unconfined columns. For example, as shown in Figure 16, longitudinal-tension-rebar of columns 1iC50 and 11C50 yielded at the load level of 0.80Pu and 0.72Pu respectively, while longitudinal-tension-rebar of columns 10C25 and 00-50 did not yield. This is a clue for the interaction between partially and fully CFRP-wrapped and longitudinal-tension-rebar. The ultimate strain of the longitudinal-tension-rebar of partially and fully CFRP-confined columns was 2.1-4.8 and 7.2-9.2 times that of the unstrengthened ones, respectively. These observations demonstrated that both partial and full wrap of CFRP sheets significantly increased the strains of longitudinal rebars.    In addition, Figure 14 also shows that stirrups of the unstrengthened columns and unconfined columns did not yield at the ultimate stage. Particularly, stirrups of columns 00-00 under concentric loads yielded at 0.98P u . This was because the deformation of the unstrengthened and unconfined columns was significantly lower than that of the strengthened columns. Therefore, these columns might fail before yielding stirrups. Meanwhile, stirrups of the partially and fully CFRP-confined columns yielded at the loading level of 0.96-0.99P u thanks to the confinement effect. These observations have proven the interaction between CFRP and stirrups. The ultimate strain of stirrups of the partially and fully CFRP-confined columns was 1.6-2.0 and 1.8-2.4 times of that of the unstrengthened ones, respectively. These observations demonstrated that the use of partial-CFRP-wrap significantly affected the lateral displacement of the columns.
The longitudinal compressive rebars of the unstrengthened columns yielded at the load level of 0.93-1.00P u (Figure 15). There, ultimate strain varied between 0.18% and 0.22% and it reduced with high e/h ratio. Meanwhile, the partially and fully CFRP-confined columns had longitudinal reinforcements yielding at the load level of 0.81-0.96P u , and 0.80-0.85P u , respectively. The ultimate strain of the longitudinal compressive reinforcements of unconfined, partially CFRP-confined, and fully CFRP-confined columns was 1.3-2.1, 1.4-3.5, and 3.6-3.8 times that of corresponding controlled ones, respectively. In addition, Figure 16 also shows that the longitudinal tension rebars of the unstrengthened and unconfined columns did not yield at the ultimate stage. Particularly, longitudinal tension rebars of column 00-5050 yielded at 0.89P u due high value of e/h ratio. This was because the deformation of these columns was significantly lower than that of the strengthened columns. Therefore, these columns might fail before yielding of longitudinal tension reinforcement and it was dependent on e/h ratio. As shown in Table 3, the longitudinal tension rebar strain of unconfined columns was even lower, achieving about 48-93% that of the corresponding controlled columns. The reason for this is that vertical CFRP sheets at the tension side work together with tension rebars. Meanwhile, longitudinal-tension-rebars of the partially and fully CFRP-confined columns yielded at the loading level of 0.72-0.96P u and 0.80-0.85P u , respectively. The use of CFRP wrap for confinement significantly reduced the axial deformation of the columns and thus delayed the yielding of longitudinal rebars as compared to the unstrengthened and unconfined columns. For example, as shown in Figure 16, longitudinal-tension-rebar of columns 1iC50 and 11C50 yielded at the load level of 0.80P u and 0.72P u respectively, while longitudinal-tension-rebar of columns 10C25 and 00-50 did not yield. This is a clue for the interaction between partially and fully CFRP-wrapped and longitudinal-tension-rebar. The ultimate strain of the longitudinal-tension-rebar of partially and fully CFRP-confined columns was 2.1-4.8 and 7.2-9.2 times that of the unstrengthened ones, respectively. These observations demonstrated that both partial and full wrap of CFRP sheets significantly increased the strains of longitudinal rebars.

Study on Design Guidelines
Two major design guidelines, namely ACI 440.2R-17 [17] of the American Concrete Institute and the Fib Bulletin 14 [18] of the International Federation for Structural Concrete, Switzerland, were selected for reviewing the prediction of CFRP-wrapped RC columns. ACI 440.2R-17 [17] does not provide the information about confinement effect of RC columns partially wrapped with FRP. Meanwhile, Fib introduced a reduction factor for taking into account the effect of partially wrapping columns.

Failure Modes Design Columns According to ACI 440.2R-17
According to ACI 440.2R-17 [17], the ultimate compressive strength of RC columns fully wrapped with FRP under pure axial compression is calculated by Equation (1).
where A g (mm 2 ) is the cross-section of the columns considering the rounded corner with a radius R c (mm) = bh − (4 − π)R c 2 , A st is the cross-sectional area of longitudinal reinforcements, f' cc is the compressive strength of confined concrete, and f y is the yield strength of longitudinal reinforcements. The effective cross-sectional area of concrete A e (mm 2 ) (see Figure 17) is estimated as follows: where A c is the cross-sectional area of concrete and ρ g is longitudinal steel reinforcement ratio.

Study on Design Guidelines
Two major design guidelines, namely ACI 440.2R-17 [17] of the American Concrete Institute and the Fib Bulletin 14 [18] of the International Federation for Structural Concrete, Switzerland, were selected for reviewing the prediction of CFRP-wrapped RC columns. ACI 440.2R-17 [17] does not provide the information about confinement effect of RC columns partially wrapped with FRP. Meanwhile, Fib introduced a reduction factor for taking into account the effect of partially wrapping columns.

Failure Modes Design Columns According to ACI 440.2R-17
According to ACI 440.2R-17 [17], the ultimate compressive strength of RC columns fully wrapped with FRP under pure axial compression is calculated by Equation (1). (1) where Ag (mm 2 ) is the cross-section of the columns considering the rounded corner with a radius Rc (mm) = bh − (4 − π)Rc 2 , Ast is the cross-sectional area of longitudinal reinforcements, f'cc is the compressive strength of confined concrete, and fy is the yield strength of longitudinal reinforcements. The effective cross-sectional area of concrete Ae (mm 2 ) (see Figure 17) is estimated as follows: where f co is the unconfined compressive strength of concrete taken as 49 MPa for the calculation and ε co is the cracking strain of concrete, taken as 0.002. Then, the ultimate strength, f cu , and ultimate strain, ε cu , can be calculated from Equations (12) where ρsg is the volumetric ratio of longitudinal reinforcement and Ag is the gross cross sectional area. The axial load carrying capacity of uniaxial-bending columns, NRd, can be calculated from Equation (18) where kc is the maximum value of N/(bhfck) ratio being derived from the Column Design Chart present in Euro Code 2 depending on the column's cross section (b and h), strength (fyk), total area (As), longitudinal steel, concrete ultimate strength taking into account confinement (fcu), denoted as fck in the Chart, d2/h = 0.22, and eccentricity (e). The axial load carrying capacity of uniaxial-bending columns, N Rd , can be calculated from Equation (18) derived in accordance with Euro Code 2 [24]. N Rd = k c bh f cu (18)  where k c is the maximum value of N/(bhf ck ) ratio being derived from the Column Design Chart present in Euro Code 2 depending on the column's cross section (b and h), strength (f yk ), total area (A s ), longitudinal steel, concrete ultimate strength taking into account confinement (f cu ), denoted as f ck in the Chart, d 2 /h = 0.22, and eccentricity (e). For biaxial-bending columns (1iC2525 and 1iC5050), the strain-compatibility method was used to compute the axial load carrying capacity including the 2nd order effects in each direction per the requirement in Euro Code 2 [24].

Comparison of Experimental Results with Design Guideline Results
The load carrying capacity of tested columns obtained from design calculations and experimental results is shown in Table 5. For full confinement columns, safety factors were between 1.87 and 1.97 when using ACI 440.2R-17 Manual [17], similar to those obtained when using Fib Bulletin 14 Guidelines [18], between 1.97 and 2.09. The differences of safety factors between these two design guides were not much, just 5-6%. However, only Fib Bulletin 14 [18] introduced a modification factor taking into account partially confined columns. The safety factors were from 1.93 to 1.98 for uniaxially loaded columns, and from 1.55 to 1.76 for biaxially loaded ones. The safety factors of biaxially loaded columns were 9-21% lower than that of uniaxially loaded columns. Therefore, more studies on this topic are deemed necessary to provide more useful data and analysis so that the design of partially FRP-confined columns can be applied with high confidence.

Conclusions
This study investigated the performance of rectangular RC columns with different patterns of CFRP-wrap subject to uniaxial and biaxial load in order to evaluate the CFRP strengthening efficiency of partially and fully confined RC columns under uniaxial and biaxial load, and to study the existing guidelines on CFRP confinement design to establish the safety factor of the predicted load-carrying capacity against the experimental results. The main findings can be summarized as follows: (1) Both partial and full CFRP wrapping demonstrated effectiveness in improving axial stiffness, load-carrying capacity, and optimization of reinforcement strains: • Initial axial stiffness of strengthened columns increased up to 17% and 37% for partially and fully CFRP-confined columns in comparison with those of corresponding controlled columns, respectively. As a result, the ultimate axial and lateral displacement of partially CFRP-confined columns increased up to 19% and 53%, and those of fully CFRP-confined columns increased up to 48% and 62%, respectively; • Load-carrying capacity of strengthened columns increased up to 31% and 33% for partially and fully CFRP-confined columns in comparing with those of corresponding controlled columns, respectively.

•
The ultimate strain of horizontal CFRP sheets varied between 0.92% and 1.13%, corresponding to 44-54% of their rupture strain from coupon tests. The difference between the CFRP strain of partial wrap columns and that of full wrap ones was small. The use of horizontal CFRP sheets delayed the yielding of compressive